Math
Graphing sine and cosine.
Definition
The process of plotting the sine and cosine functions, which produce smooth wave-shaped curves that repeat every 2π (360°). Key features include amplitude, period, phase shift, and midline.
How it works · 5 phases
Step by step.
- Identify the amplitude |a|, period 2π/|b|, phase shift −c/b, and vertical shift d from y = a·sin(bx + c) + d.
- Mark the midline at y = d.
- Plot key points: start, quarter period, half period, three-quarter period, and full period.
- Connect the points with a smooth wave curve.
- Extend the pattern in both directions as needed.
Examples
Real-world.
- 1 y = sin(x) oscillates between −1 and 1 with period 2π
- 2 y = 3cos(2x) has amplitude 3 and period π
- 3 Sound waves and tidal patterns follow sinusoidal graphs
Key Fact
y = a·sin(b(x − h)) + k: amplitude = |a|, period = 2π/|b|, phase shift = h, midline = k